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प्रश्न
In what ratio is the line joining (2, –3) and (5, 6) divided by the x-axis?
उत्तर
Let the line joining points A (2, −3) and B (5, 6) be divided by point P (x, 0) in the ratio k : 1.
`y = (ky_2 + y_1)/(k + 1)`
`0 = (k xx 6 + 1 xx (-3))/(k + 1)`
`0 = 6k - 3`
`k = 1/2`
Thus, the required ratio is 1 : 2.
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संबंधित प्रश्न
P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
Find the ratio in which the line 2x + y = 4 divides the line segment joining the point P(2, –2) and Q(3, 7).
The line joining the points (2, 1) and (5, –8) is trisected at the point P and Q. If point P lies on the line 2x – y + k = 0, find the value of k. Also, find the co-ordinates of point Q.
M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find :
- co-ordinates of M
- co-ordinates of P
- length of BP
Prove that the points A(-5, 4), B(-1, -2) and C(S, 2) are the vertices of an isosceles right-angled triangle. Find the coordinates of D so that ABCD is a square.
Show that the points A(1, 3), B(2, 6), C(5, 7) and D(4, 4) are the vertices of a rhombus.
= `a(1/t^2 + 1) = (a(t^2 + 1))/t^2`
Now `(1)/"SP" + (1)/"SQ" = (1)/(a(t^2 + 1)) + (1 xx t^2)/(a(t^2 + 1)`
= `((1 + t^2))/(a(t^2 + 1)`
`(1)/"SP" + (1)/"SQ" = (1)/a`.
The midpoint of the line segment AB shown in the diagram is (4, – 3). Write down the coordinates of A and B.
In the following figure line APB meets the X-axis at A, Y-axis at B. P is the point (4, -2) and AP: PB = 1: 2. Write down the coordinates of A and B.
From the adjacent figure:
(i) Write the coordinates of the points A, B, and
(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.
